Chapter 7 Limits Ex 7.1
Chapter 7 Limits Ex 7.1
I. Evaluate the following limits:
Question 1.
Solution:
Question 2.
Solution:
Question 3.
Solution:
II. Evaluate the following limits:
Question 1.
Solution:
Question 2.
Solution:
Question 3.
Solution:
Question 4.
Solution:
III. Evaluate the following limits:
Question 1.
Solution:
Question 2.
Solution:
Question 3.
Solution:
Question 4.
Solution:
Question 5.
Solution:
Question 6.
Solution:
Question 7.
Solution:
Question 8.
Solution:
Question 9.
Solution:
IV. In the following examples, given ∈ > 0, find a δ > 0 such that whenever, |x – a| < δ, we must have |f(x) – l| < ∈.
Question 1.
Question 2.
Question 3.
Consider ∈ > 0 and |f(x) – l| < ∈
Question 4.
Since δ can be assumed as very small, let us choose δ < 1
∴ 0 < x < 2
∴ 2 < x + 2 < 4
∴ |x + 2| < 4
∴ |(x + 2)(x – 1)|< 4 |x – 1| …..(ii)
From (i) and (ii), we get
